A210235 - OEIS

%I #4 Mar 30 2012 18:58:16

%S 1,2,1,4,4,1,7,12,7,1,12,29,28,11,1,20,64,86,56,16,1,33,132,230,210,

%T 101,22,1,54,261,560,662,451,169,29,1,88,500,1279,1860,1646,883,267,

%U 37,1,143,936,2785,4819,5257,3682,1611,403,46,1,232,1721,5848

%N Triangle of coefficients of polynomials u(n,x) jointly generated with A210236; see the Formula section.

%C For a discussion and guide to related arrays, see A208510.

%F u(n,x)=x*u(n-1,x)+v(n-1,x)+1,

%F v(n,x)=(x+1)*u(n-1,x)+(x+1)*v(n-1,x)+1,

%F where u(1,x)=1, v(1,x)=1.

%e First five rows:

%e 1

%e 2....1

%e 4....4....1

%e 7....12...7....1

%e 12...29...28...11...1

%e First three polynomials u(n,x): 1, 2 + x, 4 + 4x + x^2.

%t u[1, x_] := 1; v[1, x_] := 1; z = 16;

%t u[n_, x_] := x*u[n - 1, x] + v[n - 1, x] + 1;

%t v[n_, x_] := (x + 1)*u[n - 1, x] + (x + 1)*v[n - 1, x] + 1;

%t Table[Expand[u[n, x]], {n, 1, z/2}]

%t Table[Expand[v[n, x]], {n, 1, z/2}]

%t cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];

%t TableForm[cu]

%t Flatten[%]      (* A210235 *)

%t Table[Expand[v[n, x]], {n, 1, z}]

%t cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];

%t TableForm[cv]

%t Flatten[%]      (* A210236 *)

%Y Cf. A210236, A208510.

%K nonn,tabl

%O 1,2

%A _Clark Kimberling_, Mar 20 2012